Answers:
The two complex or imaginary roots [tex]x = i\sqrt{5}[/tex] and [tex]x = -i\sqrt{5}[/tex] have multiplicity 2.The two real roots x = 5 and x = -5 have multiplicity 3The root x = 8 has multiplicity 4======================================================
Explanation:
We'll use the zero product property to solve.
[tex]3(x^2+5)^2(x^2-25)^3(x-8)^4 = 0\\\\(x^2+5)^2=0 \text{ or } (x^2-25)^3=0 \text{ or } (x-8)^4 = 0\\\\x^2+5=0 \text{ or } x^2-25=0 \text{ or } x-8 = 0\\\\x^2=-5 \text{ or } x^2=25 \text{ or } x = 8\\\\x=\pm\sqrt{-5} \text{ or } x=\pm\sqrt{25} \text{ or } x = 8\\\\x=\pm i\sqrt{5} \text{ or } x=\pm 5 \text{ or } x = 8\\\\[/tex]
where [tex]i = \sqrt{-1}[/tex]
----------------------
The notation [tex]x=\pm i\sqrt{5}[/tex] breaks up into [tex]x=i\sqrt{5} \text{ or } x=-i\sqrt{5}[/tex]. The multiplicity of these two roots is 2 as it's the exponent of the factor [tex](x^2+5)^2[/tex]. Focus on the outermost exponent.
The notation [tex]x = \pm 5[/tex] becomes [tex]x = 5 \text{ or } x = -5[/tex]. The multiplicity of these two roots is 3 since it's the outermost exponent of the factor [tex](x^2-25)^3[/tex]
And finally, the multiplicity of the root x = 8 is 4 because it is the outermost exponent of the factor [tex](x-8)^4[/tex]
help!!! please & explain if can:(
Answer:
x = 15
Step-by-step explanation:
AEB is a right angle, a right angle is 90 degrees
this means 5x+15 needs to equal 90
plug in 15 for x
5 x 15 + 15 = 90
The temperature falls from 3 degrees Celsius to -4 degrees celcius what is the the difference in these temperatures
20 points
Answer:
7
Step-by-step explanation:
3 - -4=7
solve 3(x-4) = 12x. circle your final solution
Answer:
9x-12
Step-by-step explanation:
3*x = 3x
3*-4= -12
3x - 12 = 12x
12x-3x = 9x
9x-12
Answer: x = -4/3
Step-by-step explanation:
3(x−4)=12x
Step 1: Simplify both sides of the equation.
3(x−4)=12x
(3)(x)+(3)(−4)=12x (Distribute)
3x+−12=12x
3x−12=12x
Step 2: Subtract 12x from both sides.
3x−12−12x=12x−12x
−9x−12=0
Step 3: Add 12 to both sides.
−9x−12+12=0+12
−9x=12
Step 4: Divide both sides by -9.
-9x/-9 = 12/-9
x = -4/3
help me
the question about algebra
➡️do not inconsequential and must with and must be accompanied by steps for the process
thanks
9514 1404 393
Answer:
(x, y, z) = (8√7/105, 2√7/21, 4√7/35)
Step-by-step explanation:
The algebra is straightforward, if tedious.
We'll define X = x^2, Y = y^2, Z = z^2, -1/16 = a, -1/25 = b, -1/36 = c. Then the equations become ...
√X = √(Y +a) +√(Z +a) . . . . [eq1]
√Y = √(Z +b) +√(X +b) . . . . [eq2]
√Z = √(X +c) +√(Y +c) . . . . [eq3]
__
As with any radical equation, you square both sides, isolate the remaining radical, then square both sides again. Each squaring introduces extraneous solutions.
The equations are symmetrical, so we can do the tedious stuff on the first one, then make the appropriate substitutions to see the other two equations.
X = Y +a + 2√((Y+a)(Z+a)) +Z +a
X - Y - Z -2a = 2√((Y+a)(Z+a)) . . . . isolate the remaining radical
(X -Y -Z -2a)^2 = 4(Y+a)(Z+a) . . . . square both sides again
X^2 +Y^2 +Z^2 +4a^2 -2XY -2XZ +2YZ -4aX +4aY +4aZ = 4YZ +4aY +4aZ +4a^2
Subtracting the right side gives ...
X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4aX = 0 . . . . [eq4]
Then the remaining equations are ...
X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4bY = 0 . . . . [eq5]
X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4cZ = 0 . . . . [eq6]
Subtracting [eq6] from [eq5] gives a relation between Y and Z:
-4bY +4cZ = 0
Z = bY/c . . . . [eq7]
Substituting this into [eq4], we have ...
X^2 +Y^2 +(bY/c)^2 -2XY -2X(bY/c) -2Y(bY/c) -4aX = 0
X^2 +Y^2(1 -2b/c +(b/c)^2) -2XY(1 +b/c) -4aX = 0 . . . . [eq8]
Subtracting [eq5] from [eq4] gives a relation between X and Y:
-4aX +4bY = 0
Y = aX/b . . . . [eq9]
Substituting this into [eq8], we have ...
X^2 +(aX/b(1 -b/c))^2 -2X(aX/b)(1 +b/c) -4aX = 0
Dividing by X* gives a linear equation in X:
X(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c)) -4a = 0
X = 4a/(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c))
Substituting the above values for a, b, c, we have ...
X = 64/1575
x = √X = √(64/1575) = 8/(15√7)
Y = X(25/16)
y = x(5/4) = 2/(3√7)
Z = Y(36/25)
z = y(6/5) = 4/(5√7)
The solution is ...
x = 8√7/105 ≈ 0.201581y = 2√7/21 ≈ 0.251976z = 4√7/35 ≈ 0.302372_____
* At this point the equation is of the form pX^2 +qX = 0 or X(pX +q) = 0. One solution is X=0, which is extraneous. The solution of interest is X = -q/p.
HELP! i can not figure this out! y=4x+1
Answer:
1
Step-by-step explanation:
George hiked from the top of a hill to the valley floor. The elevation at the top of the hill is 127 feet above sea level. The valley floor is 52 feet below sea level. George stopped at a rest stop that is at an elevation exactly halfway between the top of the hill and the valley floor. What is the elevation, in feet, of the rest stop? Show your work
Answer:
The elevation of the rest stop is 37.5 feet above sea level.
Step-by-step explanation:
Given that the elevation at the top of the hill is 127 feet above sea level and The valley floor is 52 feet below sea level.
So, the total length from the top of the hill to the valley floor
[tex]l= 127+52 = 179[/tex] feet
So, length of halfway [tex]= l/2=179/2=89.5[/tex] feet ...(i)
Assuming that the stop for rest, the halfway between the top of the hill and the valley floor, is at x feet above sea level.
So, the length between the stop position and the valley floor [tex]= 52 +x[/tex] feet.
As the stop position is at half-way, so by using equation (i), we have,
[tex]52 + x = 89.5 \\\\\Rightarrow x =89.5-52 \\\\[/tex]
[tex]\Rightarrow x=37.5[/tex] feet
Hence, the elevation of the rest stop is 37.5 feet above sea level.
Find the next term of the given sequence. 1.31, 2.54, 3.77, ...
4.90
5.00
5.10
Answer:
5.00
Step-by-step explanation:
that is the question
Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of
change of money in his savings account per week?
Person to answer get prize
Pls help
Answer:
$12.5
Step-by-step explanation:
all you do is divide the 4 weeks to the $50 he earns and get $12.5 every week.
Mr. Stokes bought 6 1/2 pounds of meat for a party. He used 2 1/4 pounds of meat to make tacos. The rest he used to make 1/4 pound burgers. How many burgers did Mr. Stokes make?
9514 1404 393
Answer:
17
Step-by-step explanation:
The remaining amount of meat is ...
6 1/2 - 2 1/4 = 4 1/4 = 17/4 . . . pounds
The number of 1/4 pound burgers that can be made with that amount of meat is ...
(17/4)/(1/4) = 17/1 = 17
Mr. Stokes made 17 burgers.
what is the Symmetric property
Answer:
The Symmetric Property states that for all real numbers x and y , if x=y , then y=x . Transitive Property. The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z .
Step-by-step explanation: you couldnt have looked it up on ggle?...haha -_-'
Graph the following inequality:
Answer: the intercept is love , the slope is you , dotted or solid is <3
Step-by-step explanation:
Can someone help me with this question
Answer:
c is the right one
Step-by-step explanation:
Which of the following quotients are negative? Check all that apply.
2.2 ÷ 9.5
–0.5 ÷ 0.021
–1.3 ÷ –54.321
0.4 ÷ –0.4
Answer:
b and d
Step-by-step explanation: i did the assignment
2x-Y (5y X -6) 3^6y what is that as an expression
Answer:
The answer is:
2x + 30y^2 × 729^y
89 x 89, whats the answer?
Answer:
7921 is the correct answer
Answer:
7,291
Step-by-step explanation:
Just multiply. 89 x 89
47.9 is what percent of 152?
A)3.2%
B)31.5%
C)0.32%
D)317.3%
Answer: B
Step-by-step explanation:
Step 1: We make the assumption that 152 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100%=152
Step 4: In the same vein, x%=47.9
Step 5: This gives us a pair of simple equations:
100%=152(1).
x%=47.9(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100%/x% = 152/47.9
x= 31.5
A farmer grows a particular plant that has a gene that can be manipulated to control the age t at which the plant matures. The number of seeds S(t) produced by a plant maturing at age t is S(t)=−0.3t2+30t+0.2 seeds per mature plant A farmer asks the geneticists to genetically engineer a plant line that accounts for the fact that on his farm, only P(t)=90000t+100, plants mature to age t. What age of maturity should the geneticist select for the plants to maximize the seed production of the farmer's crop?a. Between 130 and 140 days b. Between 120 and 130 days
Answer:
The correct option is;
Between 40 and 50 days
Step-by-step explanation:
The number of seeds that are produced by a plant maturing at age t, S(t), is given as follows;
S(t) = -0.3·t² + 30·t + 0.2
The proportion of plants maturing at age (t) in the plants to be engineered by the geneticist P(t) = 90000/(t + 100)
The number of seeds produced by the plants = S(t) × P(t) = (-0.3·t² + 30·t + 0.2)×(90000/(t + 100))
To find the maximum number of seeds, we differentiate using an online tool, and equate to zero to get;
d((-0.3·t² + 30·t + 0.2)×(90000/(t + 100)))/dt = (-27000·t² - 5400000·t + 269982000)/(t + 100)² = 0
(-27000·t² - 5400000·t + 269982000)/(t + 100)² = 27000(t - 41.419)(t + 241.419)/(t + 100)² = 0
t = 41.419 or t = -241.419
Therefore, in order to maximize the production of seed of the crops of the farmer, the geneticist should select between 40 and 50 days.
Suppose AP = 2 cm and BQ = 7 cm. What is the length of PC?
Step-by-step explanation:
is this a quadrilateral? or polygon or triangle?
what are the angles (I believe there should be at least an angle given) else PC can be any value that is positive
(2x+5+8)/x-2 there should be a remainder left, pls help
Answer: 13/2
Decimal answer 6.5
im sorry if it was wrong it was what I got
Step-by-step explanation:
how come nothing feels real anymore? i've searched and i can't find why. all of my feelings and surroundings seem fake. i've felt like this for over a week straight so far, and this feeling has happened before but it's only lasted like a day or less. i can't get rid of the feeling, and i just wanna escape it. i feel like i'm not in "my" body. like my hands aren't my own, and i dont have complete control over them. when i look in the mirror, it's like it's not actually me looking back. no matter how many people are around me, it feels like they're all fake and aren't actually there. like this isn't the world i'm actually in. it's driving me insane and i just have the constant feeling that i want to cry and escape this. i can't tell my parents this, because they'll just say i'm being dramatic or just don't want to do my work or something like that. just please help me understand what's going on, or if there's anything i need to do. please. (i put this up for 50 points)
Answer:
I also have felt like this recently. Try talking to someone about it. :)
Can you help me with this?
Which of the following is a quadratic function?
A quadratic function is written as ax^2 + bx + c
Where the first term is raised to the 2nd power and the second term includes the x variable.
The answer would be number 2
The water level in a reservoir is now 52 meters. If this was a 23% increase, what was the initial depth?
Answer:
40.04
Step-by-step explanation:
It was at 40.04 before the 23% increase. To find 23 % of 52 set it up as a inequality.
x/52 = 23/100
Cross multiply
52 * 23 = 1,196 100 * x =100x
Now solve for x.
100x /100 = 1,196/100 x = 11.96
Subtract answer from 52 to get answer
52 - 11.96 = 40.04
As you can see I NEED HELP RIGHT NOW!
Answer:
Ten over two would be at the very right side of this number line. It would be located at the number 5. Negative nine over two would be located two segment or lines after negative five.
Step-by-step explanation:
Ten over two would come out to a positive and whole number of five. Negative nine over ten comes out so negative four wholes and one half. So this gets located two segments after negative five because it is not fully negative five but it is negative four and one half. I got these whole numbers by simplifying the numbers that we started off with. Hope you have an amazing day and do well on your assignments.
-Vizion
Which of the following expressions is equivalent to 3m(m - 2) - (m^2 + 1)
A. 2m^2 - 1
B. 4m^2 - 1
C. 4m^2 - 6m + 1
D. 2m^2 - 6m - 1
g(n) = 4n +4
h(n) = n +5
Find (g- h) (9)
Answer:
3n-1
Step-by-step explanation:
(4n+4) - (n+5)
i sperate it to be
4n-n and 4-5
so
3n-1 should be it
A pancake mix requires 5 cups of flour for every 10 pancakes. How much flour is used per pancake?
So you have 5 cups of flour for 10 pancakes so what you want to do is just divide 10 by 5 and you get your answer of 2 :)
in the circle shown, AB is tangent to circle o at point and OC is a radius
Which relationship is true?
Answer:
A. [tex] \overline{OC} \perp \overline{AB} [/tex]
Step-by-step explanation:
According to tangent theorem, a tangent is formed when the radius of a circle is perpendicular to the line, meeting at a point around the circle, such that the tangent line would be perpendicular to the radius of the circle with a center.
Given that [tex] \overline{AB} [/tex] is a tangent of the circle O, at a point C, and [tex] \overline{OC} [/tex] is a radius, therefore, it follows that:
[tex] \overline{OC} \perp \overline{AB} [/tex].
This means the radius of the circle is perpendicular to the tangent formed at point C.
You buy a watch for $60. a. There is a 6% sales tax. What is your total cost for the watch? b. Your friend buys the same watch a month later. It is now sold at a discount of 15%. What is the new sale price? c. What is your friend's total cost for the watch including tax? Original Price Percent of Discount Sale Price is?
Elizabeth Martz
Answer:
A= 63.6$
B= 51$
C= 54.6
D= ??? (sorry)
Step-by-step explanation:
hope this helps!
The answers to each part is given below.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that you buy a watch for $60.
{a} -Total cost of watch -
{C} = ${60 + (6% of 60)}
{C} = ${60 + (6/100 x 60)}
{C} = $(60 + 3.6}
{C} = $63.6
{b} -New sale price -
{D} = 60 - (15% of 60)
{D} = 60 - (15/100 x 60)
{D} = 60 - 9
{D} = $51
{c} -Total cost of watch including tax -
{CT} = 51 + (6% of 51)
{CT} = 51 + 3.06
{CT} = 54.06
Therefore, the answers to each part is given above.
To solve more questions on percentage, visit the link below -
brainly.com/question/24159063
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